Archive ouverte UNIGE | last documentshttps://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGEengAdaptive Boundary Conditions for Exterior Flow Problemshttps://archive-ouverte.unige.ch/unige:36369https://archive-ouverte.unige.ch/unige:36369We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computational times are typically reduced by several orders of magnitude.Tue, 06 May 2014 13:05:29 +0200Leading Order Down-Stream Asymptotics of Non-Symmetric Stationary Navier–Stokes Flows in Two Dimensionshttps://archive-ouverte.unige.ch/unige:36368https://archive-ouverte.unige.ch/unige:36368We consider stationary solutions of the incompressible Navier–Stokes equations in two dimensions. We give a detailed description of the fluid flow in a half-plane through the construction of an inertial manifold for the dynamical system that one obtains when using the coordinate along the flow as a time.Tue, 06 May 2014 13:04:54 +0200Leading Order Down-Stream Asymptotics of Stationary Navier–Stokes Flows in Three Dimensionshttps://archive-ouverte.unige.ch/unige:36367https://archive-ouverte.unige.ch/unige:36367We consider stationary solutions of the incompressible Navier–Stokes equations in three dimensions. We give a detailed description of the fluid flow in a half-space through the construction of an inertial manifold for the dynamical system that one obtains when using the coordinate along the flow as a time.Tue, 06 May 2014 13:04:24 +0200Second Order Adaptive Boundary Conditions for Exterior Flow Problems: Non-Symmetric Stationary Flows in Two Dimensionshttps://archive-ouverte.unige.ch/unige:36366https://archive-ouverte.unige.ch/unige:36366We consider the problem of solving numerically the stationary incompressible Navier Stokes equations in an exterior domain in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding so called “artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of Goldstein and Van Dyke a smooth divergence free vector field depending explicitly on drag and lift and describing the solution to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost for determining lift and drag to a given precision by typically another order of magnitude.Tue, 06 May 2014 13:03:48 +0200Adaptive Boundary Conditions for Exterior Stationary Flows in Three Dimensionshttps://archive-ouverte.unige.ch/unige:15883https://archive-ouverte.unige.ch/unige:15883Recently there has been an increasing interest for a better understanding of ultra low Reynolds number flows. In this context we present a new setup which allows to efficiently solve the stationary incompressible Navier-Stokes equations in an exterior domain in three dimensions numerically. The main point is that the necessity to truncate for numerical purposes the exterior domain to a finite sub-domain leads to the problem of finding so called “artificial boundary conditions” to replace the conditions at infinity. To solve this problem we provide a vector filed that describes the leading asymptotic behavior of the solution at large distances. This vector field depends explicitly on drag and lift which are determined in a self-consistent way as part of the solution process. When compared with other numerical schemes the size of the computational domain that is needed to obtain the hydrodynamic forces with a given precision is drastically reduced, which in turn leads to an overall gain in computational efficiency of typically several orders of magnitude.Tue, 24 May 2011 10:03:19 +0200